I kind of remember having seen this as an extension already.
And to me it sounds like something for an extension, not a default feature. (so it's a NO for me).
Not exactly what VLADYLimitLess wants I think, and not exactly what I thought I had seen either, but I found the extension which I thought was more or less in line with the Idea.
It's Profile Flair
which allows adding images based on groupmembership to the profile. The images are small but that could be edited.